The presented work of thesis has the main objective of describing the study of the landing stability of a lunar lander, accomplished through a multi-body dynamic analysis with Altair Hyperworks software package. This dissertation is the summary of a six-month work experience conducted at Thales Alenia Space Italia (TASI) in the headquarters of Turin, which is the prime contractor for the study of the European Large Logistic Lander (EL3), an independent vehicle designed for future international lunar exploration activities, envisioned as a versatile system that can support multiple and different types of mission. The landing of a vehicle on the surface of a planetary body is one of the greatest challenges in space exploration environment, since it is one of the most critical phases during a space mission.